Bulletin of the American Physical Society
69th Annual Meeting of the APS Division of Fluid Dynamics
Volume 61, Number 20
Sunday–Tuesday, November 20–22, 2016; Portland, Oregon
Session G15: Bio: Cardiovascular Flow I |
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Chair: Yasser Aboelkassem, The Johns Hopkins University Room: E143/144 |
Monday, November 21, 2016 8:00AM - 8:13AM |
G15.00001: A Hybrid Windkessel Model of Blood Flow in Arterial Tree Using Velocity Profile Method Yasser Aboelkassem, Zdravko Virag For the study of pulsatile blood flow in the arterial system, we derived a coupled Windkessel-Womersley mathematical model. Initially, a 6-elements Windkessel model is proposed to describe the hemodynamics transport in terms of constant resistance, inductance and capacitance. This model can be seen as a two compartment model, in which the compartments are connected by a rigid pipe, modeled by one inductor and resistor. The first viscoelastic compartment models proximal part of the aorta, the second elastic compartment represents the rest of the arterial tree and aorta can be seen as the connection pipe. Although the proposed 6-elements lumped model was able to accurately reconstruct the aortic pressure, it can't be used to predict the axial velocity distribution in the aorta and the wall shear stress and consequently, proper time varying pressure drop. We then modified this lumped model by replacing the connection pipe circuit elements with a vessel having a radius R and a length L. The pulsatile flow motions in the vessel are resolved instantaneously along with the Windkessel like model enable not only accurate prediction of the aortic pressure but also wall shear stress and frictional pressure drop. The proposed hybrid model has been validated using several in-vivo aortic pressure and flow rate data acquired from different species such as, humans, dogs and pigs. The method accurately predicts the time variation of wall shear stress and frictional pressure drop. [Preview Abstract] |
Monday, November 21, 2016 8:13AM - 8:26AM |
G15.00002: Finite element modeling of mass transport in high-P\'{e}clet cardiovascular flows Kirk Hansen, Amirhossein Arzani, Shawn Shadden Mass transport plays an important role in many important cardiovascular processes, including thrombus formation and atherosclerosis. These mass transport problems are characterized by P\'{e}clet numbers of up to $10^8$, leading to several numerical difficulties. The presence of thin near-wall concentration boundary layers requires very fine mesh resolution in these regions, while large concentration gradients within the flow cause numerical stabilization issues. In this work, we will discuss some guidelines for solving mass transport problems in cardiovascular flows using a stabilized Galerkin finite element method. First, we perform mesh convergence studies in a series of idealized and patient-specific geometries to determine the required near-wall mesh resolution for these types of problems, using both first- and second-order tetrahedral finite elements. Second, we investigate the use of several boundary condition types at outflow boundaries where backflow during some parts of the cardiac cycle can lead to convergence issues. Finally, we evaluate the effect of reducing P\'{e}clet number by increasing mass diffusivity as has been proposed by some researchers. [Preview Abstract] |
Monday, November 21, 2016 8:26AM - 8:39AM |
G15.00003: Modelling Cerebral Blood Flow and Temperature Using a Vascular Porous Model Stephen Blowers, Michael Thrippleton, Ian Marshall, Bridget Harris, Peter Andrews, Prashant Valluri Macro-modelling of cerebral blood flow can assist in determining the impact of temperature intervention to reduce permanent tissue damage during instances of brain trauma. Here we present a 3D two phase fluid-porous model for simulating blood flow through the capillary region linked to intersecting 1D arterial and venous vessel trees. This combined vasculature porous (VaPor) model simulates both flow and energy balances, including heat from metabolism, using a vasculature extracted from MRI data which are expanded upon using a tree generation algorithm. Validation of temperature balance has been achieved using rodent brain data. Direct flow validation is not as straight forward due to the method used in determining regional cerebral blood flow (rCBF). In-vivo measurements are achieved using a tracer, which disagree with direct measurements of simulated flow. However, by modelling a virtual tracer, rCBF values are obtained that agree with those found in literature. Temperature profiles generated with the VaPor model show a reduction in core brain temperature after cooling the scalp not seen previously in other models. [Preview Abstract] |
Monday, November 21, 2016 8:39AM - 8:52AM |
G15.00004: Computational Modeling for Fluid-Porous Structure Interaction with Large Structural Deformation Rana Zakerzadeh, Paolo Zunino In this work, we utilize numerical models to investigate the importance of poroelasticity in the interaction of blood flow with a porohyperelastic vessel wall, and to establish a connection between the apparent viscoelastic behavior of the structure part and the intramural filtration flow. The main novelty is in the design of a Nitsche's splitting strategy, which separates the fluid from the structure sub-problems for the Fluid-Porous Structure Interaction system undergoing large deformations. The general idea is to use this model to study the influence of different parameters on energy dissipation in a poroelastic medium. We also study a new benchmark test specifically designed to investigate the effect of poroelasticity on large deformations. [Preview Abstract] |
Monday, November 21, 2016 8:52AM - 9:05AM |
G15.00005: A 2D multiring model of blood flow in elastic arteries Arthur Ghigo, Pierre-Yves Lagr\'ee, Jose-Maria Fullana Three-dimensional simulations of blood flow in elastic arteries are difficult and costly due to the complex fluid-structure interactions between the motion of the fluid and the displacement of the wall. We propose a two-dimensional multiring model to overcome those difficulties and obtain at a reasonable computational cost an asymptotically valid description of blood flow in large elastic arteries. The multiring equations are derived by integrating over concentric rings of fluid a simplified system of equations based on a long wave approximation of the axisymmetric Navier-Stokes equations and a thin-cylinder description of the arterial wall. Contrary to classical one-dimensional models, obtained by integrating the same system over a single ring, the multiring model computes the velocity profile as well as the wall shear stress and requires no a priori estimation of model coefficients. We show that by numerically solving the multiring system of equations, we are able to compute a large range of classical blood flow solutions, ranging from the elastic Womersley solution to the rigid tube Poiseuille solution. [Preview Abstract] |
Monday, November 21, 2016 9:05AM - 9:18AM |
G15.00006: Secondary flow in a curved artery model with Newtonian and non-Newtonian blood-analog fluids Mohammad Reza Najjari, Michael W Plesniak Steady and pulsatile flows of Newtonian and non-Newtonian fluids through a 180$^{\circ}$-curved pipe were investigated using particle image velocimetry (PIV). The experiment was inspired by physiological pulsatile flow through large curved arteries, with a carotid artery flow rate imposed. Sodium iodide (NaI) and sodium thiocyanate (NaSCN) were added to the working fluids to match the refractive index (RI) of the test section to eliminate optical distortion. Rheological measurements revealed that adding NaI or NaSCN changes the viscoelastic properties of non-Newtonian solutions and reduces their shear-thinning property. Measured centerline velocity profiles in the upstream straight pipe agreed well with an analytical solution. In the pulsatile case, secondary flow structures, i.e. deformed-Dean, Dean, Wall and Lyne vortices, were observed in various cross sections along the curved pipe. Vortical structures at each cross section were detected using the d$_{2}$ vortex identification method. Circulation analysis was performed on each vortex separately during the systolic deceleration phase, and showed that vortices split and rejoin. Secondary flow structures in steady flows were found to be morphologically similar to those in pulsatile flows for sufficiently high Dean number. [Preview Abstract] |
Monday, November 21, 2016 9:18AM - 9:31AM |
G15.00007: High-order numerical simulations of pulsatile flow in a curved artery model Christopher Cox, Chunlei Liang, Michael W Plesniak Cardiovascular flows are pulsatile, incompressible and occur in complex geometries with compliant walls. Together, these factors can produce an environment that can affect the progression of cardiovascular disease by altering wall shear stresses. Unstructured high-order CFD methods are well suited for capturing unsteady vortex-dominated viscous flows, and these methods provide high accuracy for similar cost as low-order methods. We use an in-house three-dimensional flux reconstruction Navier-Stokes solver to simulate secondary flows and vortical structures within a rigid 180-degree curved artery model under pulsatile flow of a Newtonian blood-analog fluid. Our simulations use a physiological flowrate waveform taken from the carotid artery. We are particularly interested in the dynamics during the deceleration phase of the waveform, where we observe the deformed-Dean, Dean, Lyne and Wall vortices. Our numerical results reveal the complex nature of these vortices both in space and time and their effect on overall wall shear stress. Numerical results agree with and complement experimental results obtained in our laboratory using particle image velocimetry. [Preview Abstract] |
Monday, November 21, 2016 9:31AM - 9:44AM |
G15.00008: Color Doppler Ultrasound Velocimetry Flow Reconstruction using Vorticity-Streamfunction Formulation Brett Meyers, Pavlos Vlachos, Craig Goergen, Carlo Scalo Clinicians commonly utilize Color Doppler imaging to qualitatively assess the velocity in patient cardiac or arterial flows. However Color Doppler velocity are restricted to two-dimensional one-component measurements. Recently new methods have been proposed to reconstruct a two-component velocity field from such data. Vector Flow Mapping (VFM), in particular, utilizes the conservation of mass to reconstruct the flow. However, this method over-simplifies the influence of wall and surrounding blood motion on local measurements, which produce large, non-physical velocity gradients, requiring excessive smoothing operations to remove. We propose a new approach based on the Vorticity-Stream Function ($\psi $-$\omega )$ formulation that yields more physiologically accurate velocity gradients and avoids any added smoothing operations. Zero-penetration conditions are specified at the walls, removing the need for measurement of wall velocity from additional scans, which introduce further uncertainties in the reconstruction. Inflow and outflow boundary conditions are incorporated by prescribing Dirichlet boundary conditions. The proposed solver is compared against the VFM using computational data to evaluate measurement improvement. Finally we demonstrate the method by evaluating murine left ventricle Color Doppler scans. [Preview Abstract] |
Monday, November 21, 2016 9:44AM - 9:57AM |
G15.00009: Flow Characterization of Severe Carotid Artery Stenosis in Pre- and Post-operative Phantoms by Using Magnetic Resonance Velocimetry Seungbin Ko, Simon Song, Doosang Kim It is remained unknown that the flow characteristics changes between pre- and post-operative severe carotid artery stenosis could affect the long-term patency or failure. However, in-vivo clinical experiments to uncover the flow details are far from bed-side due to limited measurement resolutions, blurring artifact, etc. We studied detailed flow characteristics of more than 75{\%} severe carotid artery stenosis before and after surgical treatments. Real-size flow phantoms for 10 patients, who underwent carotid endarterectomy with patch/no patch closure, were prepared by using a 3D rapid-prototype machine from CT scanned images. The working fluid is a glycerin aqueous solution, and patient-specific pulsatile flows were applied to the phantoms, based on ultrasonic flow rate measurements. The flows were visualized with magnetic resonance velocimetry (MRV). The detailed flow characteristics are presented for both pre- and post-operative carotid arteries along with visualization data of 3 dimensional, 3 component velocity fields. [Preview Abstract] |
Monday, November 21, 2016 9:57AM - 10:10AM |
G15.00010: ABSTRACT WITHDRAWN |
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